A solution to the biophysical fractionation of extracellular vesicles: Acoustic Nanoscale Separation via Wave-pillar Excitation Resonance (ANSWER)

High-precision isolation of small extracellular vesicles (sEVs) from biofluids is essential toward developing next-generation liquid biopsies and regenerative therapies. However, current methods of sEV separation require specialized equipment and time-consuming protocols and have difficulties producing highly pure subpopulations of sEVs. Here, we present Acoustic Nanoscale Separation via Wave-pillar Excitation Resonance (ANSWER), which allows single-step, rapid (<10 min), high-purity (>96% small exosomes, >80% exomeres) fractionation of sEV subpopulations from biofluids without the need for any sample preprocessing. Particles are iteratively deflected in a size-selective manner via an excitation resonance. This previously unidentified phenomenon generates patterns of virtual, tunable, pillar-like acoustic field in a fluid using surface acoustic waves. Highly precise sEV fractionation without the need for sample preprocessing or complex nanofabrication methods has been demonstrated using ANSWER, showing potential as a powerful tool that will enable more in-depth studies into the complexity, heterogeneity, and functionality of sEV subpopulations.

Note S1: Brownian force and Péclet number The Brownian force applied to a nanoparticle is given by where is the Boltzmann constant; is the absolute temperature; ∆ is the magnitude of the time step; is a Gaussian random number with zero mean and unit standard deviation (69). The Brownian force will encourage the particles to spread from high-density regions to the low-density region. The Péclet number, Pe, can describe the relative importance of drag force and the Brownian force: where is the terminal velocity, is the characteristic length, is the particle diffusion coefficient, is the particle radius, is the bulk amplitude, is the speed of sound in the fluid, is the wavelength, is the displacement (70). Here, we set the terminal velocity equal to the maximum streaming velocity ( ). The characteristic length was set as 10 μm, the spacing between the channel center and collection region boundary.
can be calculated on the order of μm/s (70). We chose 5 μm/s here. Other parameters and their values are list below: , the Boltzmann constant: 1.38 × 10 , the absolute temperature: 293 K (20 ℃) , the fluid viscosity: 1.002 × 10 / (water at 20 ℃) For 100 nm polystyrene particles, the diffusion coefficient can be calculated as: = 4.28 × 10 / Choosing 10 μm as the characteristic length, the Péclet number can be calculated as: ≈ 23.36 For 30 nm polystyrene particles, the diffusion coefficient is calculated as: = 1.43 × 10 / the corresponding Péclet number is: ≈ 7.0 Similarly, the Péclet number for other particle sizes can be calculated by changing the size parameter (radius ). For sub-100 nm particles, the influence of Brownian force increases when the particle size decreases, but the drag force remains as the dominating force driving the movement of the nanoparticles.
Note S2: Acoustic simulations Numerical simulations were performed using a FEM-based computational modeling software package, COMSOL Multiphysics 5.4, to solve the acoustic field distributions and acoustic streaming present in the fluid channel and analyze the nanoparticle movement under the influence of the acoustic radiation force (55)(56)(57).
The flow motion in the channel is governed by the Navier-Stokes equations: where , , and represent the density, dynamic viscosity, and bulk viscosity of fluid, respectively; and are the fluid velocity and pressure, respectively. By applying perturbation theory, the 1 st order equations governing the acoustic field and 2 nd order equations governing acoustic streaming can be deduced as (66): In the 1 st order equations (equation (5) and (6)), , , , and are the speed of sound in the fluid, the density, shear viscosity, and bulk viscosity of fluid, respectively; and are the first order density and velocity. The acoustic pressure can be obtained using = .
In the 2 nd order equations (equation (7) and (8)), the brackets 〈•〉 indicates a time average over a harmonic oscillation period; is the second order pressure and is the second order velocity. The timeaveraged second order velocity is physically the acoustic streaming velocity. In our device, the vibration velocity of the channel floor induced by the standing SAW propagates in the y-direction and can be expressed as = ( ) (10) where is the ratio between longitudinal and transverse vibrations, is the transverse vibration amplitude of the substrate, is the decay coefficient of the vibration along the direction of the wave propagation, is the wave number of the standing SAW, and is the width of the fluid domain in y direction. In the COMSOL simulation package, the "Thermoviscous Acoustics" physics module was applied to solve the 1 st order equations. Equation (9) and (10) were applied as the velocity at the bottom of the fluid, as the boundary conditions. The impedance of the PDMS was applied to the sides and top of the channel using the "Impedance" boundary condition. The model was solved using a "Frequency Domain" solver at the resonant frequency of the device. The "Laminar Flow" physics model was applied to solve the 2 nd order equations and solved for a "Stationary" case. The "No slip" wall condition is applied to all the channel walls. More details of this simulation model can be found here (71).

Note S3: Input power evaluation
The input power can be evaluated as =

Here
is the RMS voltage in AC signal, and is the impedance. is related to the input voltage , as shown below, Therefore, the input power can be written as: The impedance can be measured and then the input power can be evaluated. Here, the impedance of our device is around 450Ω.   showing the relationship between equivalent impedance and the thickness of the PDMS wall. The equivalent impedance is influenced by the resonance of the PDMS. The equivalent impedance Zeq was calculated for increasing PDMS thicknesses in a wider range (from 15 μm to 60 μm). The first valley (I) corresponds to a resonance mode when the PDMS thickness is closest to one wavelength (λ). When the thickness increases to 1.5λ and 2.0λ, the Zeq has second (II) and third (III) resonance modes. Therefore, when the PDMS wall thicknesses are in integer multiples of half wavelength, the resonance modes will result in a local minimum value. The Zeq will increase and drop between two resonance modes. (B) Simulation of the excitation resonance frequency of the ANSWER system. The resonance frequency is obtained by calculating the eigenmodes of the system.      S8. Photomicrographs showing the changes in 100 nm polystyrene particle distribution as the particles are iteratively separated through the ANSWER device. The 100 nm polystyrene particles were loaded from the center of the channel inlet while sheath flow was loaded from two side inlets. From upper left to the lower right, the particles iterate through around 1050 virtual wave-pillars. As they flow through the chip, the 190 nm particles are moved to two sides at the outlet. Scale bar, 100 μm.       Movie S1: Visualization of acoustic virtual wave-pillars via 2 μm polystyrene particle patterns in the continuous flow. Movie S2: Visualization of acoustic streaming influence via 0.4 μm polystyrene particle patterns in the static flow.
Movie S3: Removal of the acoustic streaming effect in continuous flow verified via 0.4 μm polystyrene particle patterns. Movie S4: 190 nm polystyrene particle distribution changes as they iterate through the ANSWER device.
Movie S5: 100 nm polystyrene particle distribution changes as they iterate through the ANSWER device.
Movie S6: 50 nm polystyrene particle distribution changes as they iterate through the ANSWER device.
Movie S7: 30 nm polystyrene particle distribution changes as they iterate through the ANSWER device.